Some constructions of supermagic graphs using antimagic graphs

Abstract

A graph $G$ is called supermagic if it admits a labelling of the edges by pairwise different consecutive integers such that the sum of the labels of the edges incident with a vertex, the weight of vertex, is independent of the particular vertex. A graph $G$ is called $(a,1)$-antimagic if it admits a labelling of the edges by the integers $\{1,\dots ,|E(G)\left|\right\}$ such that the set of weights of the vertices consists of different consecutive integers. In this paper we will deal with the $(a,1)$-antimagic graphs and their connection to the supermagic graphs. We will introduce three constructions of supermagic graphs using some $(a,1)$-antimagic graphs.